Do women receive compensating wages for earnings uncertainty?

McGoldrick, Kimmarie

I. Introduction

The area of earnings uncertainty has received considerable attention in the literature. Many different measures of income uncertainty have been presented. For example, when individuals choose an occupation they face earnings uncertainty until they obtain a particular job. This uncertainty arises from the variability in earnings within an occupation. Once individuals find a job they face additional uncertainty in that jobs differ in their future earnings stability. Earnings uncertainty thus arises from the unknown wage pattern over time.

The impact of uncertainty is well documented, including its impact on wages [3; 4; 6; 7; 8]; investment in human capital [9; 12]; and occupational choice [10; 11]. The purpose of this study is to examine gender differences in compensating wages associated with income risk.(1)

The contribution of this paper to the literature on income uncertainty is the extension of the analysis to gender differences. Key to analyzing such gender differences arc the definitions and estimation procedure of systematic and unsystematic earnings. Earnings uncertainty for women is expected to be affected more by systematic, supply-side characteristics such as age, education, and migration differences for which compensating differentials are not expected. Thus, women may not receive significant compensating differentials with respect to measures of total variation when controlling for skewness in earnings.(2) Earnings uncertainty for men is expected to be influenced more by unsystematic, demand-side factors for which one would anticipate compensating differentials.

Results indicate that both men and women receive a positive wage differential for variation in unsystematic earnings when controlling for skewness. Men and women receive negative compensating differentials for positively skewed unsystematic earnings, as expected. Women receive significantly greater compensating wages for unsystematic variations in earnings than men, but are willing to give up less for the possibility of receiving higher earnings (as indicated by positive unsystematic skewness).

The next section presents the theoretical framework, reviews what has been done to date, and discusses the contribution of this paper. This is followed by a section describing the data. Section IV includes empirical results and discussions. A comparison of the findings of this paper to those in earnings uncertainty literature is provided in the concluding section.

II. Theoretical Development

This section provides theoretical support for the risk premium hypothesis and results of this paper. The model is partially based on the work of Bellante and Link [1]. A worker is assumed to maximize utility:

U = U (W, R, S, X) (1)

where W represents the worker's wages over time, R is the measure of uncertainty, S is the measure of skewness, and X represents a vector of non-wage job characteristics. The typical assumptions of [U.sub.W] [greater than] 0, [U.sub.WW] [less than] 0, [U.sub.R] [less than] 0, and [U.sub.RR] [less than] 0 are made. Additionally, it is assumed that [U.sub.S] [greater than] 0. Thus workers are assumed to be risk averse and, ceteris paribus, will prefer entering occupations which have less uncertainty about occupational earnings and that are characterized by small probabilities for receiving higher earnings.

Wages are assumed to be determined in the form of the following earnings function:

Ln [W.sub.i] = a + b [multiplied by] [R.sub.i] + c [multiplied by] [S.sub.i] + [Delta] [multiplied by] [X.sub.i] + [[Epsilon].sub.i] (2)

where Ln [W.sub.i] is the log of real wages for individual i. By maximizing (1) subject to (2), we obtain the following relationship.

L = U (W, R, S, X) - [Lambda](W - a - b [multiplied by] R - c [multiplied by] S - [Delta] [multiplied by] X) (3)

First order conditions of the Lagrangian are:

[Delta]L/[Delta]W = [U.sub.W] - [Lambda] = 0 (4)

[Delta]L/[Delta]R = [U.sub.R] + b [multiplied by] [Lambda] = 0 (5)

[Delta]L/[Delta]S = [U.sub.s] + c [multiplied by] [Lambda] = 0 (6)

[Delta]L/[Delta]X = [U.sub.x] + [Delta] [multiplied by] [Lambda] = 0 (7)

[Delta]L/[Delta][Lambda] = W - a - b [multiplied by] R - [Delta] [multiplied by] X = 0. (8)

These can be easily solved to find the following relationship:

[U.sub.W] = -[U.sub.R]/b = -[U.sub.S]/c = -[U.sub.X]/[Delta] = [Lambda] (9)

Of primary interest are the relationships of risk and skewness with wages. By solving (5) and (6) we find:

b = -[U.sub.R]/[U.sub.w] [greater than] 0 (10)

and

c = -[U.sub.S]/[U.sub.W] [less than] 0. (11)

Thus workers who face greater uncertainty will require higher wages to enter riskier occupations and will be willing to receive lower earnings for the opportunity of receiving higher incomes.

Beginning with Friedman and Kuznets [5], many authors have found a distinctive relationship between average income levels and income variability. Occupations can be classified by the level of risk as measured by the variation observed in their income distribution. Assuming risk aversion, the individuals in question will have little incentive to enter a risky occupation. If risky occupations would offer the same wage as riskless occupations, they would face a shortage of workers. Consequently, one can expect to observe compensating wages for occupational earnings risk.

The literature on earnings uncertainty is fairly small, thus a review of some of these articles is appropriate. King [7] tested whether riskier occupations offered employees higher expected average income. Risk was measured as the standard deviation of earnings within an occupation. Males, age 35-54, that had completed four years of college and were currently employed in professional occupations were examined. Compensating differentials for income variability were found to exist.

Johnson [6] used a similar approach to estimate the tradeoff between risk and average earnings across all occupations for a sample of male workers. He further stratified the sample into groups by race, age, and education levels. Risk was measured as the standard deviation of earnings within an occupation for each cohort of workers. Again, compensating wages were found for all groups.

Feinberg [3] considered the instability of earnings over time using six years of panel data for both men and women. Risk was measured as the standard deviation of the residuals from a regression over time for each individual. Results indicated that average earnings over the time period increased with risk. Gender differences indicated that women earned significantly lower compensating wages for income uncertainty. While Feinberg noted this difference, he suggested that future empirical work focusing on "how other compensating differentials vary across classes of jobs and workers" would be useful [3, 163].

In an attempt to combine the risk affects at a point in time and across time, Leigh [8] used a slightly different approach. Data consisted of white and blue collar male workers who were in the same industry over a three year period. A measure of risk was calculated that incorporated individual wage growth and industry wage variation components. Compensating wages were found to exist for white collar workers but not for blue collar workers.

Despite this literature, questions concerning earnings uncertainty remain unanswered. Gender differences in compensating differentials for income uncertainty have not been adequately considered. For example, King [7], Johnson [6] and Leigh [8] restrict their analysis to male samples. Although Feinberg [3] finds significant gender difference in risk premiums for earnings uncertainty over time, he makes no attempt to explain this result. This study extends income risk analysis by providing a possible explanation for the gender differences noted by Feinberg [3]. The distinction between systematic and unsystematic earnings uncertainty is key to these differences.

Total income variation may be separated into variation which is anticipated (or predetermined) and unexplained variation. Systematic risk includes variations in income which are either predetermined or are a result of anticipated fluctuations. Variations in earnings that are systematic arise from supply-side constraints. Variations attributable to these factors should be purged from the estimation of risk since they do not generate additional compensation in the labor market. Results obtained without eliminating this type of earnings variation will lead to an understatement of the risk premium. The discussion that follows outlines characteristics that affect systematic variation and gender differences in the impact of these characteristics.

Greater variability in earnings is more likely to occur for workers who are faced with lower employment opportunities and higher probabilities of unemployment or longer periods outside the labor market. Factors affecting these conditions which are under control of the individual or predetermined (i.e., systematic) include education, experience, number of children, marital status, discrimination, city size, and region.

Individuals with less schooling or experience confront lower employment opportunities in the labor market and are more likely to face periods of unemployment. Since it is commonly found that women have lower levels of both experience and education, one might expect women to have greater earnings variation attributable to this systematic factor.

The number of children may restrict vocational opportunities for women as a result of limited mobility. Those who work near the home for child-related reasons, out of choice or necessity, face limited employment options and it is expected that this will result in greater systematic variation in earnings.

Married women are more likely to be "tied-movers" or "tied-stayers." Thus, gender differences in the variation in earnings may be expected if locational measures contribute to differences in variation in earnings. It has been shown that there is larger variation in earnings in and across small cities than in large cities due to limited worker mobility which prevents equalization of wages [2]. There can also be differences in variation in earnings by region.

If discrimination exists, it is expected that there will be more variation in individuals' wages resulting from limited or restricted employment opportunities. These restrictions will hamper the process of wage equalization and it is expected that women will face greater variability in earnings. However, if discrimination against women is in the form of a "glass ceiling", then the variation observed will be smaller since there will be truncation at the upper end of the distribution.(3)

Unsystematic risk includes only unanticipated variations which arise from demand-side factors. Business cycle and seasonal effects on variations in earnings of workers in the construction occupation are an example. Demand-side factors are expected to affect men and women more equally since they are attributable to economy-wide conditions.(4) Unsystematic variation is expected to generate compensating differentials.

Unsystematic variation measures may be derived in two ways. Homogeneous samples provide a basis in which there is little or no variation attributable to systematic factors. This is the method applied by King [7] and Johnson [6], for example. Alternatively, systematic variation may be purged through the standard hedonic earnings function. This estimation consists of a two step procedure in which a standard earnings function is estimated and residual earnings are used to provide an estimate of unsystematic variation.

In addition to measures of variation, one might consider other moments of the income distribution to describe income uncertainty. For example, King [7] also examined skewness in the income distribution.(5) A positively skewed income distribution implies a small probability of receiving large incomes. Occupations that provide the opportunity for such large incomes will be faced with an excess of workers. Thus, a negative correlation between earnings and skewness is expected. Exclusion of skewness will understate the occupational risk premium [7,590]. Analogous [TABULAR DATA FOR TABLE I OMITTED] to unsystematic measures of variations in earnings, measures of unsystematic skewness can be derived through homogeneous samples or residuals from a standard hedonic earnings function.

Estimates of compensating differentials in this study will incorporate the concepts of systematic and unsystematic earnings in estimating variation and skewness. Specifically, compensating wages will be estimated using unsystematic variation and skewness of earnings within an occupation. Unsystematic measures will be estimated by occupation using the residuals of a standard earnings function, as described below.

III. Data Description

The analysis is based on the earnings of three-digit occupations in the United States, using the 1980 Census Public-Use Microdata Set. The national one-in-one-thousand sample was chosen. The current sample includes only 18-65 year old married and never married fulltime ([greater than or equal to] 30 hours a week; [greater than or equal to] 35 weeks a year) workers. Those living in group quarters, not identified to a SMSA, and those identified as farmers or in the military are not included. 14,605 women and 25,862 men are included in the sample. Table I describes the variables of interest and Table II reports the means and tests the differences in means of these variables. Consistent with many other studies, women have significantly lower levels of average experience, education, and wages. Women are more likely to be in Sales occupations, while men are more likely to be in Crafts occupations.

IV. Methodology and Results

Determining the relationship of risk and skewness with wages requires two steps. First, systematic earnings must be eliminated in order to derive estimates of variation and skewness based on unsystematic earnings within an occupation. The following analysis outlines the procedure for estimating unsystematic variation. Estimates of unsystematic skewness are derived in a similar manner.

Table II. Variable Means and Test of Differences in Means by Gender

Variable Men Women t-statistic

Log Earnings 2.7272 2.1987 81.16(**)
Education 12.9081 12.8533 1.83(*)
Experience 18.9824 16.6124 17.50(**)
Fertility - 1.3494
Married 0.7924 0.7003 20.29(**)
City Size 23.0969 23.7143 2.30(**)
Nonwhite 0.1338 0.1745 10.80(**)
South 0.2866 0.3024 3.35(**)
West 0.2175 0.2073 2.48(**)
North Central 0.2455 0.2421 0.77
Northeast 0.2504 0.2482 0.49
Professionals 0.1321 0.1633 8.43(**)
Managers 0.1023 0.0620 14.82(**)
Sales 0.2206 0.5174 61.10(**)
Service 0.0858 0.1251 12.19(**)
Craftsmen 0.2298 0.0280 68.82(**)
Laborer 0.2284 0.1039 34.40(**)
# of individuals 25862 14605

Notes: The number of individuals differs slightly from those
presented in the final earnings estimation since some occupations
had to be dropped in calculating measures of risk and skewness.
** and * indicate significance at the 5% 10% levels, respectively.

One method that will eliminate systematic (anticipated) variation, which has been documented previously [6; 7], uses subsamples of individuals categorized by education, age, and race. Within each of these groups, individuals are characterized by the same factors contributing to systematic variation. Thus, differences in earnings among individuals are limited to that attributable to unanticipated (demand-side or random) factors. The risk differences subsequently observed are due solely to unsystematic variation. Since a limited number of characteristics may be accounted for in this manner, an alternative measure will be suggested.

In order to control for individual characteristics as one estimates the effects of risk on individual incomes, Bellante and Link [1], and Leigh [8], suggest an alternative specification of the risk variable. Elimination of systematic variation uses residuals derived from earnings functions including regressors contributing to this risk. Bellante and Link estimated uncertainty as the coefficient of variation of residual earnings for each occupation. However, Bellante and Link used this measure only to determine what factors contributed to earnings uncertainty, not the subsequent compensation for that uncertainty as addressed here.

Leigh confined his analysis to two separate earnings functions, one for professionals and managers and the other for operatives, craftsmen, and laborers. Earnings uncertainty was estimated by industry as the standard deviation of residual earnings of the respective earnings equation. In this case, only men were included in the sample and industries rather than occupations were considered.

Two methods for estimating unsystematic variation may be employed. One approach derives unsystematic earnings from earnings functions estimated separately for broadly defined occupations or industries (by gender). These unsystematic earnings are then used to calculate the measure of unanticipated earnings variation within each occupation (again, separately for men and women).(6) This method would lead to an overcorrection in estimating the variation in each occupation. The overcorrection is a result of neglecting the variation that results from alternative choices that individuals face prior to entering an occupation. In other words, the variation would not capture all the effects with which this study is concerned.(7)

Alternatively, unsystematic earnings may be calculated from a single earnings function estimated across all occupations applied separately to men and women. Variations in unsystematic earnings are calculated for each occupation from residual earnings associated with the individuals of that occupation. The subsequent measure of risk will be a combination of variation between and within occupations since this earnings function does not control for occupational choice. This is the method applied in this paper.

The following model is used to estimate the affects of unsystematic variation in income by controlling for characteristics contributing to systematic earnings variation.

[Y.sub.ij] = [[Alpha].sub.i] + [[Beta].sub.i][X.sub.j] + [[Epsilon].sub.ij] (12)

where:

[Y.sub.ij] is the (log) annual earnings/1000 for individual j in occupation i;

[[Alpha].sub.i] is a scalar;

[[Beta].sub.i] are parameter vector estimates;

[X.sub.j] is a vector of variables affecting systematic risk of individual j (described in Table I); [[Epsilon].sub.ij] are the residuals for person j in occupation i.(8)

The earnings function is estimated separately for full-time men and women. Calculation of residual earnings depends on accurate estimation of the earnings function. Estimating the earnings equation by gender will allow for gender differences in age earnings profiles.

The vector of variables [X.sub.j] includes factors affecting systematic earnings, as discussed above. Education and experience are expected to lead to greater earnings. The age-earnings profile is expected to follow the quadratic form and thus experience will have a positive but decreasing effect on earnings. City size has been found to have a positive affect on earnings. A variable signifying race is included and it is expected that white workers will receive higher earnings than identical black workers. Locational control variables are also included. Finally, the number of children ever born is expected to have the typical adverse effect on earnings of women.

The earnings function (12), estimated across all occupations, provides parameter estimates ([[Alpha].sub.i], [[Beta].sub.i]) used to calculate the predicted (log) earnings for each individual. These coefficient estimates are presented in Table III and are consistent with findings of previous studies. Systematic earnings are estimated as the predicted earnings from this regression equation. Residual earnings are defined as the difference between actual and predicted earnings. Unsystematic earnings are calculated as the antilog of residual earnings for each individual ([[Epsilon].sub.ij]).

Earnings uncertainty in a particular occupation is measured by the standard deviation of unsystematic earnings associated with the individuals of that occupation. Each individual is then assigned the level of risk associated with their respective occupation. A measure of skewness is also calculated from unsystematic earnings within each occupation and is assigned to the respective workers. This measure of skewness is included to control for the individuals preference for positively skewed income distributions.(9)

Table III. Earnings Equations Used to Estimate Unsystematic Risk

Variable Men Women

Intercept 1.1747(**) 0.8886(**)
 (0.0211) (0.0290)
Education 0.0676(**) 0.0776(**)
 (0.0012) (0.0018)
Experience 0.0409(**) 0.0316(**)
 (0.0012) (0.0014)
Experience(2) -0.0006(**) -0.0005(**)
 (0.00002) (0.00003)
City Size 0.0013(**) 0.0020(**)
 (0.0002) (0.0002)
Fertility - -0.0445(**)
 (0.0036)
Married 0.2584(**) 0.0235(**)
 (0.0105) (0.0118)
South -0.0181(*) -0.0212(**)
 (0.0105) (0.0131)
West 0.0362(**) 0.0212
 (0.0108) (0.0138)
North Central 0.1134(**) 0.0229(*)
 (0.0104) (0.0132)
Nonwhite -0.2253(**) -0.0188
 (0.0110) (0.0125)
Adjusted [R.sup.2] 0.25 0.16
Number 25862 14605

Notes: Dependent variable is log (earnings/1000). Standard errors in
parentheses. ** and * indicate significance at the 5% 10% levels,
respectively.

Table IV presents a summary of earnings, uncertainty, and skewness categorized into that which is attributable to systematic and unsystematic factors. Men have greater total, systematic, and unsystematic earnings. Women have a greater percentage of earnings attributable to systematic factors, as expected. Men are faced with greater uncertainty in total, systematic, and unsystematic earnings but have a greater percentage of earnings uncertainty attributable to systematic factors, contrary to expectations.(10) Finally, women have greater positively skewed earnings in all three categories while the percentage attributable to systematic factors is not significantly different from [TABULAR DATA FOR TABLE IV OMITTED] the same percentage for men. Thus, the evidence indicating whether systematic factors affect the earnings of women more than men is mixed.

Table V provides an analysis of the risk and skewness an individual faces categorized by education and experience levels. This table allows for a rough analysis of uncertainty for different cohorts.

Average income uncertainty increases with education. This result indicates that men and women with higher levels of education are accepting higher levels of risk. Average income uncertainty first increases and then decreases with experience. Average unsystematic skewness decreases with education for both men and women. This implies that workers with higher levels of education are likely to face less positively skewed unsystematic earnings. Additionally, skewness increases for higher levels of experience for women but increases and then decreases for men. Married and white workers have higher levels of unsystematic risk and greater positively skewed earnings distribution compared to their respective single and nonwhite counterparts.

It is interesting to note that (in all but one case) men have significantly greater unsystematic risk and significantly less unsystematic skewness than women. These initial estimates are not intended to be a comprehensive analysis of uncertainty and skewness estimates.(11) Rather, they are provided in order to determine the patterns of unsystematic risk for various cohorts.

The incorporation of these derived measures of unsystematic risk and skewness into an otherwise [TABULAR DATA FOR TABLE V OMITTED] standard hedonic wage function will allow for compensating wage estimates. The following model is estimated separately by gender.

Ln [Y.sub.i] = a + b [center dot] [R.sub.i] + c [center dot] [S.sub.i] + [Delta][X.sub.i] + [[Epsilon].sub.i] (13)

where Y denotes earnings/1000, R represents uncertainty (as measured by the standard deviation of unsystematic earnings), S indicates the estimated skewness of unsystematic earnings, and X is a vector of individual and job characteristics.

Typical human capital variables such as schooling and experience are included in the earnings equation. Influences of these variables follow the usual assumptions. Earnings have been found to increase with city size and the same is expected to be true in this case. Location and occupational control variables are included. Individual characteristics such as marital status, race, and number of children are also included. It is expected that married workers and whites will earn more than their associated counterparts. The number of children is expected to decrease the earnings of women.

If an occupation exists in which there are no fluctuations in unsystematic income, individuals will be paid according to their characteristics. In occupations characterized by fluctuations in unexplained income, a risk exists that individuals may not receive the income that could be earned solely on the basis of their characteristics. Assuming risk aversion and limited migration opportunities, the individual will receive a premium for facing unsystematic variation. Therefore, those occupations with larger fluctuations in unsystematic earnings will pay individuals higher incomes and a positive relationship between unsystematic income variability and income will exist. Consistent with King [7], it is expected that workers would be willing to give up a portion of their income to encounter a positively skewed income distribution.

Table VI presents the results for the earnings equation estimation. Human capital variables describing experience and education have the appropriate signs and are significant for men and women. Married and white men earn significantly more than their associated male counterparts while neither of these characteristics are significant for women. The number of children significantly decreases the earnings of women. Larger city sizes significantly increase earnings, as expected. Both men and women earn significantly more in the West and North Central regions and significantly less in the Southern region compared to the omitted reference category - the Northeast region of the country. Occupational control variables suggest that both men and women earn significantly more in all occupations compared to the reference Services category.

Table VI. The Model: Ln [Y.sub.i] = a + b [center dot] [R.sub.i] +
c [center dot] [S.sub.i] + [Delta][X.sub.i] + [[Epsilon].sub.i]

Variable Men Women

Intercept 1.0233(**) 0.8373(**)
 (0.0261) (0.0337)
Risk 0.0246(**) 0.0307(**)
 (0.0012) (0.0027)
Skewness -0.0265(**) -0.0093(**)
 (0.0033) (0.0025)
Education 0.0543(**) 0.0512(**)
 (0.0015) (0.0022)
Experience 0.0404(**) 0.0291(**)
 (0.0011) (0.0014)
Experience(2) -0.0006(**) -0.0004(**)
 (0.00002) (0.00003)
City Size 0.0013(**) 0.0018(**)
 (0.0001) (0.0002)
Fertility - -0.0305(**)
 (0.0035)
Married 0.2375(**) 0.0148
 (0.0104) (0.0115)
Nonwhite -0.1954(**) 0.0123
 (0.0110) (0.0123)
South -0.0319(**) -0.0305(**)
 (0.0103) (0.0127)
West 0.0297(**) 0.0233(*)
 (0.0106) (0.0134)
North Central 0.1094(**) 0.0290(**)
 (0.0103) (0.0128)
Professional 0.2008(**) 0.4498(**)
 (0.0179) (0.0199)
Manager 0.2386(**) 0.4600(**)
 (0.0176) (0.0232)
Sales 0.1583(**) 0.2967(**)
 (0.0150) (0.0144)
Laborer 0.1814(**) 0.2307(**)
 (0.0144) (0.0190)
Craft 0.2212(**) 0.3316(**)
 (0.0145) (0.0309)
Adjusted [R.sup.2] 0.27 0.21
Number 25817 14511

Notes: Dependent variable is log (earnings/1000). Standard errors in
parentheses. ** and * indicate significance at the 5% 10% levels,
respectively.

Both men and women receive compensating wages for earnings uncertainty when controlling for skewness in unsystematic earnings. Since uncertainty is estimated as the antilog of residuals earnings, it is measured in thousands of dollars. Thus, a $1,000 increase in the standard deviation of unsystematic earnings will increase men's earnings by 2.5 percent and women's earnings by 3.1 percent. The difference in risk premium between men and women is significant at the one percent level.

As stated above, if workers prefer a positively skewed (unsystematic) earnings distribution, they will receive negative compensating wages as skewness increases. The coefficient on the skewness of unsystematic earnings is negative and significant for both men and women, consistent with expectations. Like the measure of uncertainty, this variable is measured in thousands of dollars. Men are willing to forego 2.7 percent of their income for an increase in skewness by $1,000 whereas women are only willing to forego 0.9 percent of their income. The difference in earnings that men and women are willing to forego is significant at the one percent level.

V. Conclusion

These results are consistent with previous studies that have found positive and significant compensating wages for income uncertainty [3; 6; 7; 8]. They are also consistent with findings that suggest workers are willing to give up earnings for a small probability of receiving greater earnings (as indicated by a positively skewed unsystematic earnings distribution) [7].

The findings differ from previous work by Feinberg [3] with respect to the magnitude of the risk premium paid to men and women. Feinberg found that women received lower risk premiums than men, yet in the current study women are found to receive significantly greater risk premiums for earnings uncertainty. These results are not necessarily inconsistent. In the work by Feinberg, systematic earnings are not purged from the estimate of earnings uncertainty and a measure of skewness is not included in the estimation of risk premiums. As suggested above, each of these factors will lead to understatement of risk premiums and their effects are expected to be greatest for women. These two factors could contribute to women's lower risk premium as found by Feinberg.

In addition, the measures of uncertainty in the current context and that of Feinberg differ significantly. While Feinberg measures uncertainty over time, the current study considers uncertainty over occupations. Indeed, future work may focus on the implications of differing definitions of income uncertainty and the resulting differences in estimated risk premiums by gender.(12)

1. I use the terms "uncertainty" and "risk" interchangeably.

2. This is true even if women receive significant compensating differentials with respect to unsystematic measures of variation since inclusion of systematic variation will lead to an understated risk premium.

3. This problem is somewhat resolved by including skewness to capture other distributional differences in addition to variation.

4. The exception to this would be the demand for goods from particular occupations which are more male or female concentrated.

5. Since the literature typically defines income risk as the variability in earnings, I will continue with this standard and refer to skewness as a separate concept.

6. Leigh [8] used a similar approach estimating earnings functions for managerial and professional occupations separately from operators, craftsman, and labor workers.

7. Estimation of the earnings function separately by broad industry and occupational categories (and gender) was performed and results were consistent with those present below. Results available upon request.

8. The traditional assumptions for [[Epsilon].sub.ij] (identically distributed within occupations and expected value equal to zero) are made.

9. Note that in this procedure, occupations containing less than three individuals are dropped from the analysis at this stage since there are insufficient observations to calculate skewness.

10. One possible explanation for this seemingly contradictory result is the exclusion of any control for labor force participation. If women adjust to labor market conditions by altering their level of labor force participation, one would expect those earning low wages to drop out more often than those earning high wages. The tendency to drop out will decrease the observed variation in earnings. Unfortunately, the Census data does not provide any reasonable control for labor force participation.

11. This is the case since many factors affecting these estimates are not held constant.

12. In a current working paper by this author these differences are under investigation. Using a sample of the PSID similar to Feinberg's original sample, both earnings uncertainty over time and over occupations are analyzed. Preliminary results suggest that while earnings uncertainty measured over time indicates women having significantly lower risk premiums, unsystematic earnings uncertainty measured over occupations (including a measure of skewness) indicates no significant gender differences in risk premium.

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